To solve this problem, we need to determine the total number of children who responded to the survey given that 600 of them represent 60% of the total respondents. Here's a step-by-step solution:
1. Understand the given information:
- 600 children favor chocolate.
- This number (600) represents 60% of the total respondents.
2. Convert the percentage to a proportion:
- 60% can be written as a proportion: [tex]\( \frac{60}{100} = 0.6 \)[/tex].
3. Set up the equation to find the total number of respondents:
- Let [tex]\( T \)[/tex] be the total number of respondents.
- Given that 600 children represent 60% of the total, we can write the equation:
[tex]\[
0.6 \times T = 600
\][/tex]
4. Solve for [tex]\( T \)[/tex]:
- To find [tex]\( T \)[/tex], divide both sides of the equation by 0.6:
[tex]\[
T = \frac{600}{0.6}
\][/tex]
5. Calculate the total number of respondents:
- When we perform the division:
[tex]\[
T = 1000
\][/tex]
So, the total number of children who responded in the survey is 1000.
Answer:
The total number of respondents in the survey is 1000 children.
